What is the integral of sqrt(1-x) ?

The integral of sqrt(1-x) is -2/3 (1-x)^{3/2}+C

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integral of sqrt(1-x)

\int 1 - x d x

- \frac{2}{3} (1 - x)^{\frac{3}{2}} + C

Solution steps

\int 1 - x d x

Apply u-substitution

: \int - u d u

= \int - u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= - \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 - x

= - \frac{2}{3} (1 - x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (1 - x)^{\frac{3}{2}} + C

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3} t

x \to \infty lim (\frac{8}{x})

(- 1, 3), (13, 1)

\int \frac{tan ( x )}{cos ^{2} ( x )} d x

8 t \frac{d y}{d t} + y = t^{4}

What is the integral of sqrt(1-x) ?
The integral of sqrt(1-x) is -2/3 (1-x)^{3/2}+C